A hemisphere is placed on top of an inverted cone. The back of the circumference, the radius, and the perpendicular height of the cone are marked with dashed lines. The radius and the height make a right angle and are perpendicular.
An engineer wants to know the volume of the following object composed of a hemisphere and a cone. She knows the height of the cone is equal to the diameter of the hemisphere, and the volume of the cone is 12 m3 . What is the volume of the whole object?(1 point)
Responses
18 m3
24 m3
There is not enough information to say.
36 m3
36 m3
To find the volume of the entire object, we need to add the volume of the hemisphere and the volume of the cone.
Volume of cone = 1/3 * π * r^2 * h
Volume of cone = 12 m^3
Since the radius and height of the cone are equal, we can substitute h = 2r into the volume formula:
12 = 1/3 * π * r^2 * (2r)
12 = 2/3 * π * r^3
r^3 = 18/π
r = (18/π)^(1/3)
Now, the volume of the hemisphere can be calculated as:
Volume of hemisphere = 2/3 * π * r^3
Volume of hemisphere = 2/3 * π * (18/π)^(1/3)^3
Volume of hemisphere = 2/3 * π * 18 = 12 π
Therefore, the total volume of the entire object is:
12 π + 12 = 36 m^3